时滞反馈与多频激励联合作用下Duffing振子的快慢动力学
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1.南通大学 理学院,南通,226019;2.江苏大学 理学院,镇江,212013

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国家自然科学基金项目(面上项目,重点项目,重大项目)


Fast-slow dynamics of Duffing oscillator under the combination of time-delay feedback and multi-frequency excitations
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1.School of Science,Nantong Universtiy, Nantong 226019, China;2.School of Science,Jiangsu University,Zhenjiang 212013,China

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    摘要:

    研究了状态时滞反馈与多频混合激励联合作用下Duffing振子模型的非线性动力学。 通过讨论特征方程根的分布情况,给出了时滞系统分岔条件,得到时滞量和反馈增益的分岔曲线,揭示了系统稳态解的共存与动力学转迁方式。结合数值算例,揭示系统在不同参数条件下的快慢动力学行为。结果表明,时滞量及其反馈增益可以显著影响系统的多尺度效应,调谐多频激励幅值亦可以改变快慢变流形的动态特性,从而使得Duffing振子产生不同振荡模式下的复杂动力学行为。

    Abstract:

    The nonlinear dynamics of Duffing oscillator with state delay feedback and multi-frequency excitations was studied. By discussing the distribution of the characteristic equation roots, bifurcation conditions of time-delay system were discussed. The parametrical regions about the time-delay and feedback coefficient were obtained, from which the critical transition conditions among different coexisting attractors are revealed. Fast- slow dynamics of the system under different parameters were explored. The results show that the time delay and its feedback gain can significantly affect the characteristics of multiple time scale system. Moreover, the tuning of multi-frequency excitations can also act on the dynamical characteristics by changing the slow manifold.

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王东梅,余跃,张正娣.时滞反馈与多频激励联合作用下Duffing振子的快慢动力学[J].动力学与控制学报,2021,19(1):35~44; Wang Dongmei, Yu Yue, Zhang Zhengdi. Fast-slow dynamics of Duffing oscillator under the combination of time-delay feedback and multi-frequency excitations[J]. Journal of Dynamics and Control,2021,19(1):35-44.

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历史
  • 收稿日期:2019-08-07
  • 最后修改日期:2019-11-21
  • 录用日期:2019-12-15
  • 在线发布日期: 2021-03-08
  • 出版日期: 2021-02-20

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